Introduction to Logarithms

A Presentation by Jeremy Kass, sans degrees

Logarithms:
An Introduction

Logarithms:
An Introduction

Definition of Logarithms

What are logarithms?

Put simply, logarithms are the inverse function of the exponential function. This can be expressed as such:

What are the parts of them?

Logarithms are divided into three parts, represented here by three variables. The argument (c) tells us what power (b) we have to raise the base (a) to.

Logarithm Restrictions

Do logarithms have a restricted domain?

Yes, logarithms have a restricted domain. They cannot calculate values for c that are not positive in the real numbers system. To input negative values, you must go to the complex world.

Do logarithms have restrictions for bases?

Yes, logarithms have restrictions for their bases. Their bases must be a positive real number that is not equivalent to 0 or 1 to return real values for b. Logarithms with negative bases or bases of one can only be calculated in the complex world.

Do logarithms have restrictions for outputs?

No, logarithms can output any real or complex value.

Do logarithms have restrictions for bases?

Yes, logarithms have restrictions for their bases. Their bases must be a positive real number that is not equivalent to 0 or 1 to return real values for b.

Rules for Logarithms

How many rules are there?

There are seven (7) important rules to logarithms. They are the following: the product rule, the quotient rule, the power rule, the base-change rule, the inverse exponentiation rule, the inverse logarithmic rule, and the rules for bases.

What is the product rule?

What is the quotient rule?

What is the power rule?

What is the base-change rule?

What is the inverse exponentiation rule?

What is the inverse logarithmic rule?

What are the rules for bases?

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